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Joe Posnanski has written another thoughtful piece on the divide between writers of a statistical bent and those who prefer the evidence of their eyes. I highly recommend it; Posnanski distills the arguments into one about stories. Do statistics ruin them? His answer is no. Obviously, one should use statistics to tell other stories, if not necessarily better ones. He approached this by examining how one statistic, “Win Probability Added”, helped him look at certain games with fresh eyes.

My only comment here is that, I’ve noticed on his and other sites (such as Dave Berri’s Wages of Wins Journal) that one difficulty in getting non-statisticians to look at numbers is that they tend to desire certainty. What they usually get from statisticians, economists, and scientists are reams of ambiguity. The problem comes not when someone is able to label MichaelJordan as the greatest player of all time*; the problem comes when one is left trying to place merely great players against each other.

* Interestingly enough, it turns out the post I linked to was one where Prof. Dave Berri was defending himself against a misperception. It seems writers such as Matthew Yglesias and King Kaufman had mistook Prof. Berri’s argument using his Wins Produced and WP48 statistics, thinking that Prof. Berri wrote other players were “more productive” than Jordan. To which Prof. Berri replied, “Did not”, but also gave some nuanced approaches in how one might look at statistics. In summary, Prof. Berri focused on the difference in performance of Jordan above that of his contemporary peers.

The article I linked to about Michael Jordan shows that, when one compares numbers directly, care should be taken to place them into context. For example, Prof. Berri writes that, in the book Wages of Wins, he devoted a chapter to “The Jordan Legend.” at one point, though, he writes that

in 1995-96 … Jordan produced nearly 25 wins. This lofty total was eclipsed by David Robinson, a center for the San Antonio Spurs who produced 28 victories.

When we examine how many standard deviations each player is above the average at his position, we have evidence that Jordan had the better season. Robinson’s WP48 of 0.449 was 2.6 standard deviations above the average center. Jordan posted a WP48 of 0.386, but given that shooting guards have a relatively small variation in performance, MJ was actually 3.2 standard deviations better than the average player at his position. When we take into account the realities of NBA production, Jordan’s performance at guard is all the more incredible.

If one simply looked at the numbers, it does seem like a conclusive argument that Robinson, having produced more “wins” than Jordan, should be the better player. The nuance comes when Prof. Berri places that into context. Centers, working closer to the basket, ought to have more, high-percentage shooting opportunities, rebounds, and blocks. His metric of choice, WP48, takes these into consideration. When one then looks at how well Robinson performed above his proper comparison group (i.e. other centers), we see that Robinson’s exceptional performance is something one should expect when comparing against other positions but is not beyond the pale when compared to other centers. However, Jordan’s performance, when compared to other guards, shows him to be in a league of his own.

That argument was accomplished by taking absolute numbers (generated for all NBA players, for all positions) and placing them into context (comparing to a specific set of averages, such as by position.)

This is where logic, math, and intuition can get you. I don’t think most people would have trouble understanding how Prof. Berri constructed his arguments. He tells you where his numbers came from, why there might be issues and going against “conventional wisdom”, and in this case, the way he structured his analysis resolved this difference (it isn’t always the case he’ll confirm conventional wisdom – see his discussions on Kobe Bryant.)

However, I would like to focus on the fact that Prof. Berri’s difficulties came when his statistics generated larger numbers for players not named Michael Jordan. (I will refer people to a recent post listing a top-50 of NBA players on Wages of Win Journal.*)

* May increase blood pressure.

In most people’s minds, that clearly leads to a contradiction: how can this guy, with smaller numbers, be better than the other guy? Another way of putting this is: differences in numbers always matter, and they matter in the way “intuition” tells us.

In this context, it is understandable why people give such significance to 0.300 over 0.298. One is larger than the other, and it’s a round number to boot. Over 500 at-bats, the difference between a 300-hitter and a .298-hitter translates to 1 hit. For most people who work with numbers, such a difference is non-existent. However, if one were to perform “rare-event” screening, such as for cells in the blood stream that were marked with a probe that “lights” up for cancer cells, then a difference of 1 or 2 might matter. In this case, the context is that, over a million cells, one might expect to see, by chance, 5 or so false-positives in a person without cancer. However, in a person with cancer, that number may jump to 8 or 10.

For another example: try Bill Simmons’s ranking of the top 100 basketball players in his book, The Book of Basketball. Frankly, a lot of the descriptions, justifications, arguments, and yes, statistics that Simmons cites looks similar. However, my point here is that, in his mind, Simmons’s ranking scheme matters. The 11th best player of all time lost something by not being in the top-10, but you are still better off than the 12th best player. Again, as someone who works with numbers, I think it might make a bit more sense to just class players into cohorts. The interpretation here is that, at some level, any group of 5 (or even 10) players ranked near one another are practically interchangeable in terms of their practicing their craft. The differences between two teams of such players is only good for people forced to make predictions, like sportswriters and bettors. With that said, if one is playing GM, it is absolutely a valid criterion to put a team of these best players together based on some aesthetic consideration. It’s just as valid to simply go down a list and pick the top-5 players as ordered by some statistic.* If two people pick their teams in a similar fashion, then it is likely a crap shoot as to which will be the better team in any one-off series. Over time (like an 82-game season), such differences may become magnified. Even then, the win difference between the two team may be 2 or 3.

* Although some statistics are better at accounting for variance than others.

How this leads back to Posnanski is as follows. In a lot of cases, he does not just simply rank numbers; partly, he’s a writer and story teller. The numbers are not the point; the numbers illustrate. Visually, there isn’t always a glaring difference between them, especially when one looks at the top performances.

Most often, the tie-breaker comes down to the story, or, rather, what Posnanski wishes to demonstrate. He’ll find other reasons to value them. In the Posnanski post I mentioned, I don’t think the piece would make a good story, even if it highlighted his argument well, had it ended differently.

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Although this blog is ostensibly about books, I’ve written a lot about sports, mostly dealing with how non-scientist readers perceive statistical analysis of athlete productivity. This issue fascinates me; I think how people think about sports statistics provides a microcosm in how they may respond to similar treatments in the scientific realm. Economists, mathematicians, engineers and physicists will provide a better explanation of the analysis than I can. Instead, I want to focus on the people who draw (shall we say) interesting conclusions about research.

In a recent podcast, Bill Simmons interviewed Buzz Bissinger on the BS Report (July 28, 2010). Bissinger gained some negative exposure as he had railed against the blogosphere and sports analysis. In this podcast, Bissinger was given some time to elaborate on his thoughts. He most certainly is not a raving lunatic, but he did say a few things that I find representative of how statistical analyses are often misinterpreted by non-scientists (and even scientists.)

Bissinger took the opportunity to trash Michael Lewis’s Moneyball, mostly by pointing out how Billy Beane isn’t so smart, and that all in the end, the statistical techniques didn’t work – only Kevin Youkilis – mentioned in the book, had proven to be a success. I think that misses the point. Yes, the book documents the tension between the scouts and the stat-heads. I think Lewis chose this approach to make the book more appealing, by taking the human interest angle, than simply writing a technical description of Beane’s “new” approach. Perhaps Lewis overstates the case in showing how entrenched baseball GMs were in relying on eyeball and qualitative skill assessments, but the point I got from the book was that: Beane worked under money constraints. He needed a competitive edge. Most baseball organizations relied on scouts. Beane thought that to be successful, he needed to do something different (but presumably had some relevance) to provide baseball success.

Beane could have used fortune tellers; I think the technique in Moneyball (i.e. statistical analysis) is besides the point. Beane found something that was different and based more of his decisions on this new evaluation method. This is a separate issue from how well the new techniques performed. the first issue is whether the new technique told him something different. As it happens (as documented in Moneyball, Bill James’s Baseball Abstracts, and by many sports writers and analysts), it did. The result is that Beane was able to leverage that difference – in this case, he valued some abilities that others did not – and signed those players to his roster. The assumption is that if his techniques couldn’t give him anything different from previous methods of evaluation, than he would have had nothing to exploit.

The second point is whether the techniques told him something that was correct. And again, the stats did provide him with a metric that has a high correlation with winning baseball games – the on-base percentage. So one thing he was able to exploit was the perception in value of batting average (BA) versus on-base percentage (OBP). He couldn’t sign power hitters: GMs – and fans – like home runs. He avoided signing hitters with high BA and instead signed those with high OBP.

This led to a third point: Beane can only leverage OBP to find cheap players (and still win) so long as there were few GMs doing the same. Of course the cost of OBP will increase if others come onboard and have deep pockets (like the Yankees and the Red Sox.) So Beane – and other GMs – would have to become more sophisticated in how they draft and sign players. Especially if they work under financial constraints. As my undergraduate advisor said, “You have to squeeze the data.”

One valid point point Bissinger made was that the success of the Oakland A’s coincided with the Big Three pitchers. So clearly, Bissinger wrote off a significant amount of Oakland success to the three. That’s fine, as the question can be settled by looking at data. What annoyed me is when readers do not pay attention to the argument. I just felt that Moneyball was more about how one can find success by examining what everyone else is doing, and then doing something different. The only constraint is whether something different would bring success.

I felt that Bissinger is projecting when he assumes that using stats means the rejection of visual experience. The importance of Moneyball is in demonstrating that one can find success by simply finding out what people have overlooked. Once the herd follows, it makes sense to seek out alternative measures, or, more likely, to find out what others are ignoring. If the current trend is on high OBP and ignoring pitchers with a high win-count, then a smart GM needs to exploit what is currently undervalued. Statistics happens to be one such tool – but it isn’t the only tool.

And part of the reason I write this is, again, to highlight the fact that people usually have unvoiced assumptions about the metrics they use. The frame of reference is important. In science, we explicitly create yardsticks for every experiment we perform. We assess things as whether they differ from control. It is a powerful concept. And even if the yardstick is simply another yardstick, we can still draw conclusions based on differences (or even similarities, if one derives the same answer by independent means.)

This brings me to recent Joe Posnanski and DavidBerri posts. The three posts I selected all demonstrate the internal yardsticks (hidden or otherwise) that people use when they make comparisons. I am a fan of these writers. I think Posnanski has provided a valuable service in bridging the gap between analysis and understanding, facts and knowledge. Whether one agrees or disagrees with his posts, I think Posnanski is extremely thoughtful and clear about his assumptions and conclusions, which facilicates discussion. The post has a simple point: Posnanski wrote about “seasons for the ages.” A number of readers immediately wrote to him, complaining about how just about anyone who hits 50 home runs in a season would qualify. To which Posnanski coined a new term (kind of like a sniglet) – obviopiphany.He realized that most people simply associate home runs with a fantastic season for a hitter. That isn’t what Posnanski meant, and in the post he offers some correction.

The Posnanski post has a simple theme and an interesting suggestion: the outrage over steroids may be due to the fact that people assume that home run hitters are good hitters. Since steroids help power, the assumption is that steroids make hitters good – which in most cases simply means more home runs. But Posnanski – and others sabermetricians – propose that one must hit home runs in the context of getting fewer strikeouts and more walks. The liability involved in striking out more, and not walking, is too much and washes out the gains made from hitting the ball far. Thus Posnanski posts names a 5 players who are not in the Hall of Fame, and aren’t home run hitters, but who nevertheless produced at the plate – according to some advanced hitting metrics. I won’t go into this more, except to say that here, Posnanski makes his assumptions clear. He uses OBP+, wins above replacement player, and other advanced metrics to make his point. But it is telling that Posnanski had to stitch together the assumptions his readers had – that the yardstick for good hitting simply boils down to home runs.

The Berri posts describe something similar. One of them is from a guest contributor, Ben Gulker, writing about how Rajon Rondo was not going to be selected for Team USA in the world championship because he doesn’t gather enough points. The other highlights how the perception of Bob McAdoo changed as a function of the fortunes of his team. Interestingly enough, McAdoo became a greater point getter while becoming a less efficient shooter and turning the ball over more; at the same time, his reputation was burnished by the championships his teams won.

The story has been told many times by Berri. It seems that in general, basketball writers and analysts associate good players as those who score points (in the literal sense, regardless of shooting percentage) and who played on championship teams. There are several problems here. Point getting must take place in the context of a high shooting percentage. One must not turn the ball over, one must rebound, one must not commit an above average number of fouls, and hopefully get a few steals and blocks. I don’t think anyone would disagree that such a player is a complete player and ought to be quite desirable, regardless of how many championship rings he has or if he scores only 12 points a game. Berri has examined this issue of yardsticks, and he has found that what sports writers, coaches, and GMs think of players has an extremely high correlation with, simply, how many points they get (this is shown by what the writers write and how they vote for player awards, how often coaches play someone, and how much GMs pay players.) The verbiage writing up about the defensive prowess and the “little things” are ignored when the awards are given and fat contracts handed out. Point getters get the most accolades and the most money.

And the other point is how easily point getters reflect the luster of championships. Nevermind that no player can win alone, but this again is an example of how people end up with not only unspoken yardsticks, but also choose a frame of reference without analyzing if it is the correct one. The reference point is a championship ring. As has been documented, championships are not good indicators of good teams. The regular season is. This is simply due to sample sizes. More games are played in the regular season. Teams are more likely to arrive at their “true” performance level than in a championship tourney with a variable number of games – and frankly where streaks matter. A good team might lose four games in a row, in the regular season, but they may lose only 10 for the year. In a tournament, they would be bounced out if they lose four in a series.

In this context, the Premier League system in soccer makes sense. The best teams compete in a regular season; the team with the best record is the champion. So people who assume that a point-getter who plays on a championship is better than a player who shoots efficiently (but with fewer points) and rebounds/steals/blocks/does not turnover above average, and on a non-champion team, make two errors. They selected the wrong metric twice over.

With that said, I could only have made that point because of newer metrics that provide another frame of reference. Moreover, the new metrics tend to have improved predictive abilities over simply looking at point-getting totals. Among the new metrics, there are some that show a higher correlation with the scoring difference (and thus win/loss record) of teams. It doesn’t matter what they are, but an important point is that one can derive these conclusions about which metric is better or worse.

This is the main difference in scientific (of which I include athlete productivity analysis) and lay discourse. In the former, the assumptions are made bare and frames discussion. A good scientific paper (and trust me, there are bad ones) makes excruciatingly detailed descriptions of controls, the points of comparisons, any algorithms/formulae, and how things are compared. In the lay discourse, this isn’t the standard one would use, because communicating scientific findings to other scientists use a stylized convention. Using such a mode of communication with friends would make one a bore and a pedant – not to mention one would become lonely real quick.